Angles and constructions
Drawing lines and quadrilaterals
Two tools, two jobs. A set square gives you a right angle instantly; a protractor gives you any angle you like.
Drawing a perpendicular line
WITH A SET SQUARE: put one edge along the line, then draw along the other edge. The two edges are already at 90°, so the new line is perpendicular. WITH A PROTRACTOR: put the centre mark of the flat edge at the point, so that the 90° marker sits on the line. Then draw along the flat edge. Both give the same result — the set square is quicker, the protractor works for any angle.
Through a given point
To draw a perpendicular through a particular point B on the line, place the set square so its edge runs along the line AND passes through B, then draw. With a protractor, line the original line up with the 90° mark and draw along the flat edge.
Drawing parallel lines a set distance apart
To draw a line parallel to another and exactly 5 cm from it: 1. Draw a perpendicular line, using a set square or protractor. 2. Measure 5 cm along that perpendicular. 3. Draw the new line through that point, perpendicular to the SAME perpendicular. Because both lines are at 90° to the same line, they must be parallel — and the 5 cm you measured is the distance between them.
Drawing a quadrilateral accurately
Use a ruler for the lengths and a protractor for the angles. Draw one side first, then measure the angle at each end before drawing the next side. Check as you go: the four angles must total 360°. If yours do not, something has been measured wrongly.
Worked examples
Drawing a perpendicular with a set square
- Put one edge of the set square along the line.
- Draw along the other edge.
Answer: The two edges are already at 90°
Drawing a perpendicular with a protractor
- Put the centre of the flat edge at the point.
- Line the 90° marker up with the line.
- Draw along the flat edge.
Answer: A line at 90° to the original
A perpendicular through a given point B
- Place the set square so its edge runs along the line AND through B.
- Draw.
Answer: A perpendicular passing through B
A line parallel to another, 5 cm away
- Draw a perpendicular to the first line.
- Measure 5 cm along it.
- Draw a new line perpendicular to that same perpendicular.
Answer: Both are at 90° to the same line, so they are parallel
Drawing a quadrilateral accurately
- Ruler for the lengths, protractor for the angles.
- Draw one side, then measure the angle at each end.
Answer: Check the four angles total 360°
Your four angles come to 350° — what now?
- A quadrilateral's angles must total 360°.
- So something has been measured wrongly.
Answer: Measure them again
Where you see this in real life
- Setting out a rectangular flower bed uses exactly this: one side, then two perpendiculars, then measure equal distances.
- The lines on a sports pitch are drawn perpendicular to each other for the same reason — accuracy at the corners.
Key words
- Protractor
- an instrument for measuring and drawing angles
- Set square
- a triangular tool with a built-in right angle
- Perpendicular
- at 90° to another line
- Parallel
- always the same distance apart
- Construct
- draw accurately with instruments
- Ruler
- the instrument for measuring and drawing lengths
- Quadrilateral
- a shape with four straight sides